9.4-two - 2. Find 21 Position Vector An algebraic vector v...

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Unformatted text preview: 2. Find 21 Position Vector An algebraic vector v is represented as; where u and h are real numbers (scalars) called the components of the vector v. Theorem Suppose that v is a vector with initial point P1 = (x1. yi). not. necessarily the origin. and terminal point P3 = (x3. yg). If v = Png. then v is equal to the position vector Equality of Vectors Two vectors v and w are equal if and only if their corresponding components are equal. That is, If v = ((11,171) and w = ((12,!)2) then v = w if and only if a] = (12 and bl = b2. . I X r (1,0) i=('1$0)andj=(0~.1> v = (a,b) = (20,0) + b(0. 1) = ai + bj -3 -3 <2‘3> :: QL+3J 3. Add and Subtract Vectors Algebraically Let v = ali + blj = (at. b1) and w = azi + bgj = ((13. 1);) be two vectors.and let a be a scalar. Then v + w = (a1 + az)i + (b1 + b31i=<a1 + “2171 + b2) V —w= (a; —a3)i + (131 —bz)j :( 1‘02-51 ‘bfl (aafli + (ab;)j : (aa;.cxb1) M = W? + b? V + V" = (a1 + a2ji+(b1+ : <01 + (12. b} + b2) (31 + a2, [71 + be) (32‘ b2) 0 (IV I (aafli + (abflj = (adhcvbl) V: sign-9w 525165” w» v) -—) *—? -° "7 h) E) h? 3 45,4.) _2¢2;5‘7 41%, ~52 +44, 40) <r47~l£7 ...
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9.4-two - 2. Find 21 Position Vector An algebraic vector v...

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